Friday, September 25, 2009

Two Fillomino puzzles

Now for something a little different. I usually post free-form word puzzles, but there's a much more popular class of puzzles which includes things like crosswords and Sudoku. I am against Sudoku on principle, but there are other kinds, such as Fillomino, which are very good.

1. Divide the grid into polyominoes that satisfy the following rules.
2. Every number in the grid must be contained in a polyomino containing that quantity of squares.
3. No two polyominoes containing the same quantity of squares may share an edge. (If every square were numbered according to the quantity of squares in its corresponding polyomino, no two identical numbers will ever be on opposite sides of an edge.)
4. A polyomino may contain one, more than one, or none of the numbers originally given.
The puzzle and instructions were swiped from A Cleverly-Titled Logic Puzzle Blog (which I highly recommend), but Fillomino itself was created by Nikoli.

So long story short, I wrote one of these Fillomino puzzles and it's hosted on the aforementioned blog. It's, uh, probably a bit too difficult, given that I just introduced Fillomino above. But I like it, so here it is.

If you need hints, or have comments or solutions, you may send any images to me at skepticsplay at gmail dot com.

Solutions to these puzzles will not be posted on the blog later.


Eduard said...

This remembers me an online Rubik game where differently colored pairs of squares in a grid had to be joined by a chain. What was the name of this game?

miller said...

It sounds like you are talking about Hyper Frame. Hyper Frame is essentially Number Link on the surface of a cube. Number Link is also a very good puzzle.

Eduard said...

I didn't know Hyper Frame. Thanks.
It's exactly the same idea I met in a 2-dim Rubik game.

Ólafur Jens Sigurðsson said...

hmm ... it looks like your Fillomino is unsolvable. I say this because just by looking at the lower right corner I see the following setup:

* 3 1
1 * *
2 * *

where * is an empty cell.

The only way I can find to fill in this corner is the following way:

* 3 1
1 3 3
2 2 *

but this leaves the cell furthest to the right and at the bottom empty and no way to fill it.

Am I missing something here?

miller said...

Polyominoes need not contain any of the originally given numbers. Therefore, you could simply place a 1 in the lower right corner.

Norwegian Shooter said...

1. What is the principle that causes you to be against Sudoku?
2. Would this principle be of use against Ken Ken?
3. Can you point me to some starter puzzles?

miller said...

Why I don't like sudoku: I find it to be one of the driest of grid-filling puzzles. You can solve it just by applying a bunch of rules, without really thinking about the logic behind those rules.

I don't particularly like ken ken either, but it's better than sudoku.

Some sites I'd recommend are A Cleverly-Titled Logic Puzzle Blog, as mentioned above, and PuzzlePicnic. Google works too.

Mark Erickson said...

I actually forgot the could-be-interesting question. Why are these grid puzzles always have a point of symmetry at the central point. Did I say this right? Do you know what I mean?

miller said...

The symmetry about the center is basically for artistic purposes. Writers have a lot of freedom when writing these puzzles, so they might as well make it symmetrical. In these fillomino puzzles, we first chose the locations of all the givens, and then chose the numbers that would be given.

Actually, a lot of puzzles, such as Masyu, are not usually symmetrical. That's because the writers have less freedom in writing them, so can't always afford to use such arbitrary constraints.

Anonymous said...

You could also play easier sudoku puzzles online at

dartheye said...

woo, i just finished both! pretty simple =D